On the width and shape of gaps in protoplanetary disks

By A. Crida, A. Morbidelli, F. Masset. 2005

453 citations recorded by the source corpus.

Although it is well known that a massive planet opens a gap in a protoplanetary gaseous disk, there is no analytic description of the surface density profile in and near the gap. The simplest approach, which is based upon the balance between the torques due to the viscosity and the gravity of the planet and assumes local damping, leads to gaps with overestimated width, especially at low viscosity. Here, we take into account the fraction of the gravity torque that is evacuated by pressure supported waves. With a novel approach, which consists of following the fluid elements along their trajectories, we show that the flux of angular momentum carried by the waves corresponds to a pressure torque. The equilibrium profile of the disk is then set by the balance between gravity, viscous and pressure torques. We check that this balance is satisfied in numerical simulations, with a planet on a fixed circular orbit. We then use a reference numerical simulation to get an ansatz for the pressure torque, that yields gap profiles for any value of the disk viscosity, pressure scale height and planet to primary mass ratio. Those are in good agreement with profiles obtained in numerical simulations over a wide range of parameters. Finally, we provide a gap opening criterion that simultaneously involves the planet mass, the disk viscosity and the aspect ratio.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/df9f58880bc41de035496c9c806d0af5f341add1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

Citations in the corpus

Resolved gas cavities in transitional disks inferred from CO isotopologs with ALMA (2015, background): “The outcome of the gradual drop model is particularly interesting because it better resembles the shape of the gap carved by a planet, as seen in planet-disk interaction simulations (Crida et al. 2006; Zhu et al. 2011; de Juan Ovelar et al. 2013; Fung et al. 2014).”
TRANSITIONAL DISKS AS SIGNPOSTS OF YOUNG, MULTIPLANET SYSTEMS (2011, methodology): “Our order-of-magnitude estimate of maximum gap width agrees with the numerical work of Crida et al. (2006).”
THE MASS–METALLICITY RELATION FOR GIANT PLANETS (2015, background): “Gap opening and the planetary starvation that results remains a topic of continuing research (e.g., Crida et al. 2006; Fung et al. 2014; Duffell & Dong 2015).”
WEAK TURBULENCE IN THE HD 163296 PROTOPLANETARY DISK REVEALED BY ALMA CO OBSERVATIONS (2015, background): “The threshold for a massive planet to open a gap within the disk depends on the ability of the accretion flow to refill the gap; weaker turbulence, and hence a weaker accretion flow, would allow smaller planets to open large disk gaps (Crida et al. 2006; Kley & Nelson 2012; Fung et al. 2014).”
The Non-carbonaceous–Carbonaceous Meteorite Dichotomy (2020, background): “When Jupiter reached a mass of ∼ 50 M⊕, a gap opened in the disk (Crida et al. 2006), leading to inward migration of Jupiter (Walsh et al. 2011).”
LkCa 15: A YOUNG EXOPLANET CAUGHT AT FORMATION? (2011, background): “When a planet clears a gap in its disk, then the size of the gap should be approximately equal to the planet’s Hill radius (Crida et al. 2006); even if the planet is ∼10 MJup, then its Hill radius is only ∼2–3 AU.”
The dynamics of Jupiter and Saturn in the gaseous protoplanetary disk (2007, methodology): “In Section 3 we use the algorithm of Crida et al. (2007) to investigate how the dynamics of the Jupiter–Saturn couple depends on the disk’s aspect ratio and viscosity, and also on numerical parameters such as disk’s resolution and smoothing length.”
Cavity opening by a giant planet in a protoplanetary disc and effects on planetary migration (2007, methodology): “Equation (14) of Crida et al. (2006) provides a way of computing semi-analytically the density profile of a gap for any disc and planet parameters.”
ALMA continuum observations of the protoplanetary disk AS 209. Evidence of multiple gaps opened by a single planet (2017, background): “Nonetheless, the depth of the gap is sensitive to disk viscosity, with planets opening deeper gaps in low viscosity disks (Crida et al. 2006; Zhu et al. 2013).”
Small vs. large dust grains in transitional disks: do different cavity sizes indicate a planet? - SAO 206462 (HD 135344B) in polarized light with VLT/NACO (2013, background): “Disk−planet interaction can result in spiral density waves (e.g. Tanaka et al. 2002) and possibly generate both a disk gap and a spiral arm structure (Crida et al. 2006).”
Ring shaped dust accumulation in transition disks (2012, methodology): “FARGO has been used for numerous studies of disk evolution (e.g., Crida et al. 2006; Zhu et al. 2011; Regály et al. 2011).”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, background): “(6) The parameter P is given by Crida et al. (2006) as P = 3 4 H rH + 50 qR ≤ 1 .”
Rapid inward migration of planets formed by gravitational instability (2011, background): “The gap-opening criterion for a planet on a fixed circular orbit in a laminar viscous disc takes the form (Crida et al. 2006) 1.1 ( q h3 )−1/3 + 50 (α h )( q h3 )−1 .”
Separating gas-giant and ice-giant planets by halting pebble accretion (2014, background): “This was expected because for a disc undergoing perturbations by a small planet, the resulting disc structure is dominated by disc’s internal pressure and hence its aspect ratio (Crida et al. 2006).”
THE RUNTS OF THE LITTER: WHY PLANETS FORMED THROUGH GRAVITATIONAL INSTABILITY CAN ONLY BE FAILED BINARY STARS (2009, background): “Rewriting equation (24) we find the ratio of gap width to Hill radius is: ∆ RH = ( fgq πα r2 H2 )1/3 (26) Note that ∆ > RH recovers the canonical gap opening estimate appropriate for Jupiter: q > 40ν/(r2Ω), modulo order unity coefficients (cf. Crida et al. 2006).”
THE IMPRINT OF EXOPLANET FORMATION HISTORY ON OBSERVABLE PRESENT-DAY SPECTRA OF HOT JUPITERS (2016, methodology): “We use the transition criterion of Crida et al. (2006) to determine a planet’s migration regime.”